Just so it's clear, NSA is technically part of DoD. (Though it's a bit like FBI's relation to DOJ, they operate very independently.)

Also, the DoD CIO has had, since ~2003, this excellent FAQ supporting open source:

http://dodcio.defense.gov/Open-Source-Software-FAQ/

But as people on this thread and elsewhere will tell you, that hasn't resulted in widespread support at DoD for open source.